A system with unity feedback is shown in figure 1 Where Gs

A system with unity feedback is shown in figure (1), Where G(s) = 6/s(s + 3). Calculate the percentage overshoot, settling time (2% criterion) and the steady state value of the response of the output of the system when the input is a unit step input. Use MATLAB to simulate the output response. Include all the MATLAB codes in your answers.

Solution

S = stepinfo(y,t,yfinal) takes step response data (t,y) and a steady-state value yfinal and returns a structure S containing the following performance indicators:

RiseTime — Rise time

SettlingTime — Settling time

SettlingMin — Minimum value of y once the response has risen

SettlingMax — Maximum value of y once the response has risen

Overshoot — Percentage overshoot (relative to yfinal)

Undershoot — Percentage undershoot

Peak — Peak absolute value of y

PeakTime — Time at which this peak is reached

For SISO responses, t and y are vectors with the same length NS. For systems with NU inputs and NY outputs, you can specify y as an NS-by-NY-by-NU array (see step) and yfinal as an NY-by-NU array. stepinfo then returns a NY-by-NU structure array S of performance metrics for each I/O pair.

S = stepinfo(y,t) uses the last sample value of y as steady-state value yfinal. S = stepinfo(y) assumes t = 1:ns.

S = stepinfo(sys)computes the step response characteristics for an LTI model sys (see tf, zpk, or ss for details).

S = stepinfo(...,\'SettlingTimeThreshold\',ST) lets you specify the threshold ST used in the settling time calculation. The response has settled when the error |y(t) - yfinal| becomes smaller than a fraction ST of its peak value. The default value is ST=0.02 (2%).

S = stepinfo(...,\'RiseTimeLimits\',RT) lets you specify the lower and upper thresholds used in the rise time calculation. By default, the rise time is the time the response takes to rise from 10 to 90% of the steady-state value (RT=[0.1 0.9]). Note that RT(2) is also used to calculate SettlingMin and SettlingMax.